Gravity turn/ja

gravity turn(重力ターン)とは最少の燃料消費で打ち上げから機体を周回軌道に投入させるまでの操縦技法である。機体を離陸させるためには重力より高い加速度で押し上げる必要がある。In order to maintain a stable orbit, the craft must have enough sideways momentum at a high enough altitude to avoid colliding with any surface features or getting slowed down by the atmosphere, if any. A gravity turn combines these two steps into one maneuver, saving fuel in the process. As a craft starts ascending vertically, it slowly turns to the side until by the end of the turn it points sideways.

類推するなら重力ターンを一切せず周回軌道に乗る状況を想像するとわかりやすい: その場合垂直に上昇した後で、90°旋回し軌道に乗ることになる。これに対し重力ターンはこの90°コーナーを手前でショートカットする状態に当たる。これで短縮できた経路分が燃料節約につながる。

この効率性は地表に降下する場合にも適用できる。水平方向の速度を相殺してから垂直にゆっくり降下するより、斜め方向に噴射して水平垂直両方向を同時に相殺したほうが実際は効率が良い。

力学

離陸時の合力

機体を30°傾けた状態の合力

Gravity turns work by fighting gravity the least amount possible to gain enough altitude and horizontal speed for the desired maneuver. Since the gravity of the local celestial body is always pulling on the craft, it will always accelerate most slowly when pointing directly away from that body and would accelerate faster in any other direction than straight vertical. If a launched craft followed a purely vertical flight path, then it would spend all of its thrust accelerating in the slowest direction, effectively spending the most Delta-V to gain the least speed without gaining any lateral speed necessary to orbit. In other words, a straight vertical launch is the least efficient launch.

The gravity turn maneuver is accomplished as follows. Assuming a perfectly flat launch site, the maneuver begins as a vertical launch, then once a certain altitude is reached, a slight turn is made. By turning away from vertical slightly, gravity will pull the velocity vector of the craft down towards that direction and the craft will tilt to follow it. As this happens, the craft will gain more speed sooner since it is travelling in a vector that is not directly opposed to gravity, effectively saving fuel and time. The farther the vector tilts to the side, the percentage of thrust spent fighting gravity becomes smaller and the percentage of thrust spent gaining speed becomes larger. Since the majority of this vector change is done by gravity and not by the flight controls, another tiny amount of fuel is saved. By the end of the gravity turn, no fuel is wasted fighting gravity. If the craft has gained enough lateral speed at an altitude above any mountains or atmosphere, it then begins a stable orbit.

The altitude to start a gravity turn at depends on several factors. On bodies with atmospheres, drag also comes into determining the most efficient gravity turn.

タイミング

重力ターンにおける機体の傾斜開始タイミングと傾斜量は主に3つの要素に基づく:

1. 飛行経路上の障害物の有無
2. 大気の密度
3. 天体の重力ひいては機体の推力重量比 (TWR)

丘や山などに差し掛かる経路は明らかに避けるべきである。障害物を避けるように経路を設定することで効率が下がるかもしれないが、墜落するよりは効率が良い。

On bodies with no atmospheres, a launched craft need not worry about any drag generated, and thus should turn to face near horizontal as early as possible given its TWR and the height of nearby surface features. Doing this minimizes the percentage of thrust spent resisting gravity, while maximizing the percentage of thrust spent gaining enough horizontal speed to achieve orbit.

On planets with an atmosphere however, timing and amount of tilt are crucial to the success and efficiency of a gravity turn. If a craft turns too late or too little in its flight, it will waste more fuel fighting gravity than would be used resisting drag. If a craft turns too early or too far, it will travel a longer distance through the atmosphere, losing more speed to drag, requiring more fuel to regain that lost speed. If such a turn results in the craft pointing horizontal before arriving at an altitude above the atmosphere, then the craft will have to spend more delta-V to gain the necessary altitude, if the TWR of the current stage allows it. If not, then it will result in an inevitable surface collision.

The gravity strength of the local body also comes into effect. On bodies with very strong gravity wells, a larger portion of thrust must be spent fighting gravity, leaving a smaller portion of thrust to spend gaining altitude and lateral speed. On such a body, that means a high turn at a narrow angle. Conversely, on a body with very light gravity, the turn can be low at a sharper angle. The craft's TWR also affects when to begin a turn. Crafts with very high TWRs will have plenty of thrust to spare, so they can spend a smaller percentage of their thrust fighting gravity and a larger percentage gaining lateral speed. This means that such a craft can make their gravity turns lower and sharper than a craft with a low TWR.

Gravity turns are not always perfect. The most efficient gravity turn will have a continuous burn right up to completing circularization. Factors like TWR changing as the craft flies and human reaction time keep them from being perfect. In such a scenario, the craft may need to pause its burn once any atmosphere is escaped, coast to apoapsis and then do a circularization burn.

For an example of proper turn timing and amount, the most efficient gravity turn on Kerbin begins around 10 kilometers, with the ship and vector marker facing 30 to 40 degrees above the artificial horizon.

推力重量比

推重比は重力ターンに大きな影響を持つ要素である。燃料を燃焼することで機体の推重比は次第に上がっていく。また推重比はステージ移行でタンクを切り離せば上がりエンジンを切り離せば下がる。If the craft is following too sharp a gravity turn, it could completely exhaust its more powerful beginning stages before escaping the atmosphere and advance to a stage meant for a higher altitude but now has a TWR too low to fight gravity, eventually leading to a surface collision. If the craft follows too narrow a gravity turn, it could spend its more powerful beginning stages reaching an altitude above the atmosphere, but then advancing to a stage with a TWR not powerful enough to properly circularize and orbit, eventually re-entering the atmosphere and colliding with the ground.

See also

• Gravity turn on Wikipedia